Population dynamics: from rare events to evolution

Rare events are by definition difficult to observe, and their numerical study is all the more complex. A class of methods, "population dynamics algorithms" allowed progress in this area. The idea is to simulate not one, but a large number of copies of the system, each playing the role of an 'individual' possessing a certain 'genome' (the configuration); these individuals are subject to 'mutation' (noise) and 'selection' (birth/death). This selection makes it possible to make typical, in the population dynamics, the rare event in which we are interested in the dynamics of the original system. Population dynamics are in exact correspondence with models of biological phenomena in genetics and ecology – studied in mathematics. The aim of the workshop is to exploit this correspondence to put in contact researchers of different expertise, in order to (i) export modern tools and concepts from the theory of large deviations (dynamic phase transitions) and algorithms (effective dynamics) to biological models, so as to understand its hidden characteristics; (ii) conversely to import mathematical tools from probability theory to improve the existing algorithms of the theory of large deviations (such as the study of genealogy, the role of rare mutations, and the effects of finite population size).